At a given instant in an airplane race, airplane A is flying horizontally in a s

Question

At a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its speed is being increased at the rate of 8m/s2. Airplane B is flying at the same altitude as airplane A and, as it rounds a pylon, is following a circular path of 300m radius. At the given instant the speed of B is being decreased at the rate of 3m/s2. Set a x-y rectangular coordinate system (with unit vectors i and j [The bold letters means vectors]) (a) Determine the instantaneous velocity vector for each airplane under this (b) Determine the instantaneous acceleration vector for each airplane under this (c) Determine the tangent and normal components of the instantaneous acceleration (d) Determine the relative acceleration vector of B with respect to A. coordinate system. coordinate system. vector for each plane. 450 km/h 300 m 30° 540 knh

Explanation / Answer

a)

airplane A :

VA = (450 km/h) i + 0 j = 125 i + 0 j

airplane B :

VB = (540 Cos60) i + (- 540 Sin60) j = 150 i - 130 j

b)

Instanteneous acceleration of airplane A is given as

aA = 8 i + 0 j

Instanteneous acceleration of airplane B is given as

aB = (- 3 Cos60 ) i + (3 Sin60) j = - 1.5 i + 2.6 j

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